CN112880659A - Fusion positioning method based on information probability - Google Patents

Fusion positioning method based on information probability Download PDF

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CN112880659A
CN112880659A CN202110026669.8A CN202110026669A CN112880659A CN 112880659 A CN112880659 A CN 112880659A CN 202110026669 A CN202110026669 A CN 202110026669A CN 112880659 A CN112880659 A CN 112880659A
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张怡
宋哲
唐成凯
张玲玲
程泽宇
于阳
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement

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Abstract

The invention provides a fusion positioning method based on information probability, which comprises the steps of deducing a parameter analytic expression of a new probability density function after two probability density functions are fused, deducing a parameter analytic expression of fusion of a plurality of sources by a recursion method, and calculating and obtaining fusion navigation positioning information by using the fused parameter analytic expression. Compared with the traditional fusion positioning method based on Kalman filtering, the method not only can reduce the calculation amount of fusion positioning and improve the operation speed, but also is more flexible in the expansion of the fusion navigation source and has strong robustness on the access and disconnection of the navigation source. As can be seen from simulation results, the method can improve the positioning precision after fusion, and the more the fusion sources are, the higher the precision is. The method provides a new idea for the design of the fusion navigation positioning algorithm, and can acquire the fused navigation positioning information more quickly and in real time.

Description

Fusion positioning method based on information probability
Technical Field
The invention belongs to the field of fusion positioning, and particularly relates to a fusion positioning method based on information probability.
Background
From the 20 th century to the 21 st century, satellite navigation (GNSS) has gone through the process from the beginning of mao lu to the development of sound, and has evolved from a main body of application of satellite navigation to a new stage of integration of positioning, navigation, time service with information carriers such as mobile communication and the internet. Because GNSS signals are easily interfered, research organizations in many countries and regions have developed a plurality of researches to make up the shortage of GNSS as a target, thereby ensuring the battle ability of troops in various environments. Because each navigation system can bring certain influence to navigation positioning precision when working independently, the defects of each navigation system when working independently are overcome by adopting a combined navigation mode at present, and the advantages of each navigation system can be brought into full play, thereby obviously improving the navigation performance of the combined system. And the fusion algorithm employed therein plays a crucial role.
In life, in order to enable navigation terminal carriers such as automobiles, airplanes and ships to be positioned more accurately, various navigation sensors are often installed on the carriers, the navigation data formats of the sensors are usually not uniform, and a fusion algorithm is needed to fuse the navigation data, so that more accurate navigation positioning information is obtained. Most of the traditional fusion algorithms are developed based on Kalman Filtering (Kalman Filtering) and improved algorithms thereof, and observation data is input and output through a system so as to carry out optimal estimation on the system state. In the document 'continuous positioning based on GPS/INS/magnetometer multi-sensor fusion, technical report on sensing, 2020, vol.33, No.9, pp.1320-1326', GPS and INS signals are fused by using Kalman filtering, and INS signals are corrected by using magnetometers, so that the information of the magnetometers cannot be fused by an overall fusion algorithm due to the weak expandability of a fusion method based on the Kalman filtering; if more than two navigation source information are fused, Kalman filtering calculation is complex and slow, and the real-time performance of the navigation information cannot be guaranteed.
Disclosure of Invention
In order to solve the problems that the traditional fusion algorithm based on Kalman filtering is poor in expandability and complex in calculation and cannot ensure real-time performance under the condition of excessive fusion sources, the invention provides a novel method for fusion positioning by using probability density functions of navigation source information.
The technical scheme of the invention is as follows:
the fusion positioning method based on the information probability comprises the following steps:
step 1: for n navigation sources loaded on a carrier, establishing a probability statistical model of the positioning information of each navigation source, and determining a probability density function of the positioning information of each navigation source; the probability density function is based on a gaussian distribution;
step 2: the carrier runs for a period of time T-1, 2, …, T, and the motion trail sequence of the carrier measured by the ith navigation source is Xi＝{xi1,xi2,…,xiT}，i＝1,2,…,n；
And step 3: calculating a fusion product factor S between every two navigation sources by using the probability density function of the positioning information of each navigation source determined in the step 1 and the motion trail sequence of the carrier measured by each navigation source in the step 2 through the following formulaab
Figure BDA0002890486440000021
Wherein the content of the first and second substances,
Figure BDA0002890486440000022
and
Figure BDA0002890486440000023
two navigations for calculationVariance of probability density function of sources a and b, xaAnd xbPositioning the measured values for the navigations corresponding to the two navigation sources a and b;
if more than s fusion product factors in the fusion product factors between a certain navigation source and other navigation sources are lower than a set threshold value, the navigation source is considered to have larger deviation in the task, and the data corresponding to the navigation source is removed before the subsequent fusion calculation is carried out, so that the navigation source does not participate in the subsequent fusion calculation;
and 4, step 4: after all navigation sources are processed in step 3, the formula is utilized
Figure BDA0002890486440000024
Calculating to obtain a carrier position coordinate P obtained by fusion at the t-th momentt(ii) a Wherein m is the number of the navigation sources subjected to fusion after the processing of the step 3, and xitVehicle position information measured at time t for the ith navigation source.
Further, in step 3, s is 2.
Further, in step 1, when the navigation source is a navigation source with known positioning accuracy, the standard deviation RMS is calculated to be 1.2 × CEP according to the circular probability error CEP of the navigation source, and the corresponding variance σ is further obtained2＝1.44*CEP2。
Further, in step 1, when the navigation source is a navigation source with unknown positioning accuracy, a fixed-point multiple-iteration experimental method is used to obtain the positioned data distribution, the circular probability error CEP of the navigation source is determined, then the standard deviation RMS is calculated to be RMS 1.2 CEP, and the corresponding variance σ is further obtained2＝1.44*CEP2。
Advantageous effects
The navigation positioning performance of a single navigation source is improved to the bottleneck, and the overall navigation positioning precision can be effectively improved by fusing the information of a plurality of navigation sources and then performing navigation positioning; the traditional fusion positioning method based on Kalman filtering has the problems of large difficulty in navigation source number expansion and complex calculation, and the expansion and real-time calculation of the navigation source under fusion positioning are seriously restricted. Compared with the traditional fusion positioning method based on Kalman filtering, the fusion positioning method based on the information probability not only can reduce the calculation amount of fusion positioning and improve the operation speed, but also is more flexible in the expansion of a fusion navigation source and has strong robustness on the access and disconnection of the navigation source. As can be seen from simulation results, the method can improve the positioning precision after fusion, and the more the fusion sources are, the higher the precision is. The method provides a new idea for the design of the fusion navigation positioning algorithm, and can acquire the fused navigation positioning information more quickly and in real time.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of fusion positioning using information probability;
FIG. 2 is a schematic diagram of a circular probability error;
FIG. 3 illustrates measurement and fusion trajectories under scenario one;
FIG. 4 illustrates an error curve for scenario one;
FIG. 5 illustrates error values for scenario one condition;
FIG. 6 shows measurement and fusion trajectories under scenario two;
FIG. 7 error curves for scenario two;
figure 8 scenario two conditions for error values.
Detailed Description
In order that the technical means of the invention may be more readily understood, the invention will now be further described with reference to specific examples.
There is a carrier, on which several navigation signal sources are loaded, the initial position coordinates are (10m,15m), and the speed v of the carrier in the x-axis directionx5m/s, speed v in y-axis directionyThe positioning accuracy of the navigation source 1 is 5m, the positioning accuracy of the navigation source 2 is 10m, and the positioning accuracy of the navigation source 3 is 12m at 8 m/s. The vehicle moves for a total of 50s, and each navigation source provides navigation positioning data every 1 s. With the above conditions as background, simulation was performed with reference to the system flow shown in fig. 1.
The method comprises the following steps: establishing a probabilistic statistical model of navigation source signals
To build a probabilistic statistical model of the navigation source location information, the probability distribution characteristics of its location are clarified first. The positioning probability of most navigation sources is in a Gaussian distribution, so how to solve the distribution parameters is the most important factor. GNSS navigation source positioning accuracy units are typically given in terms of a circular probability error (CEP), e.g. a CEP of 5m, meaning that a circle is drawn with a radius of 5m, 50% of the points can fit within the circle, i.e. the probability of GNSS positioning at 5m accuracy is 50%.
Navigation sources are mainly classified into the following two categories: a parameter-known navigation source and a parameter-unknown navigation source. The positioning probability characteristic of the navigation source is usually gaussian-shaped distribution characteristic, so that the variance of the probability distribution is usually required to be obtained. For navigation sources with known parameters, the positioning accuracy is generally known and is generally characterized by a circular probability error (CEP) that is scaled to the standard deviation (RMS) by: RMS 1.2 CEP. Calculating to obtain corresponding standard deviation and then obtaining corresponding variance, namely sigma2＝1.44*CEP2. For a navigation source with unknown parameters, a fixed-point multiple-iteration experiment method is usually adopted to obtain a positioned data distribution, a circle is drawn by a radius R according to the data center position, and if 50% of data points fall within the range of the circle, the radius R is called a circle probability error (CEP) of the navigation source, as shown in fig. 2. The corresponding variance expression is as follows: sigma2＝1.44*R2。
Step two: fusion algorithm of probability information
And performing fusion multiplication on the navigation source positioning information according to the established probability statistical model of the navigation source positioning information. Because the established probability density function of each navigation source positioning information is based on Gaussian distribution, the probability distribution after fusion multiplication is also Gaussian distribution, and the navigation positioning information after fusion can be obtained according to the parameter information of the probability density function after fusion.
First, the result of fusion multiplication of two probability density functions is studied, and two Gaussian distributions are assumed to exist
Figure BDA0002890486440000051
And
Figure BDA0002890486440000052
the expressions are respectively:
Figure BDA0002890486440000053
Figure BDA0002890486440000054
the product of the two is:
Figure BDA0002890486440000055
by simplifying equation (3) and converting to standard form, the following results can be obtained:
Figure BDA0002890486440000056
in the formula (4), each parameter expression is as follows:
Figure BDA0002890486440000057
Figure BDA0002890486440000058
Figure BDA0002890486440000059
in the formulas (5) to (7), the formula (5) gives the mean value of the fused probability density function, the formula (6) gives the variance of the probability distribution after fusion, and the formula (7) represents a fusion factor, represents the level of the fusion result, and can be used for judging the quality of the fusion result subsequently.
When the number of the fused probability density functions exceeds two, the expression parameters after the fusion of the n probability density functions can be deduced by adopting a recursion relation, and the mean value mu after the fusion of the n probability density functionsFSum variance
Figure BDA00028904864400000510
The derived expression is as follows:
Figure BDA0002890486440000061
Figure BDA0002890486440000062
in the formula, muiIs the mean of the ith probability density function,
Figure BDA0002890486440000063
is the variance of the ith probability density function.
Therefore, when there are n navigation sources, the probability density function corresponding to each navigation source location is respectively
Figure BDA0002890486440000064
The probability density function expression after the fusion of the navigation sources is as follows:
Figure BDA0002890486440000065
wherein the content of the first and second substances,
Figure BDA0002890486440000066
μfis the mean of the fused probability density functions,
Figure BDA0002890486440000067
is the variance of the fused probability density function.
Step three: navigation source information fusion positioning
For n navigation sources mounted on a carrier, the carrier runs for a period of time T equal to 1,2, …, T, and the motion track sequence of the carrier measured by the ith (i equal to 1,2, …, n) navigation source is Xi＝{xi1,xi2,…,xiT}. And (3) utilizing the navigation positioning information obtained by the navigation sources through measurement and the previously established probability statistical model corresponding to the navigation sources to represent the measurement value as an expected value in the probability statistical model, fusing through the fusion algorithm of the probability density function mentioned in the second step to obtain the fusion positioning information of all the navigation sources at each moment, and forming a fusion navigation positioning track by the navigation positioning information fused at each moment.
Further, before fusion, the validity of the navigation source needs to be determined, and a fusion product factor S between two navigation sources can be obtained by using formula (7)ab：
Figure BDA0002890486440000068
In the formula (I), the compound is shown in the specification,
Figure BDA0002890486440000069
and
Figure BDA00028904864400000610
is the variance, x, of two probability density functionsaAnd xbThe measurements are located for navigation corresponding to the two navigation sources.
The formula (11) is used for calculating a fusion product factor between every two navigation sources, and then a certain threshold M is set for judgment. If one of the navigation sources is connected withThe fusion product factors between every two other navigation sources are more than two (>2) If the value is lower than the threshold value M, the navigation source is considered to have larger deviation or failure in the task, and the data corresponding to the navigation source is removed before the subsequent fusion calculation is carried out, so that the navigation source does not participate in the subsequent fusion calculation. After data corresponding to the problem navigation source is eliminated, the carrier position coordinate P obtained by fusion at the t-th moment can be obtained by using a formula (8)tComprises the following steps:
Figure BDA0002890486440000071
wherein x isitAnd measuring the position information of the ith navigation source at the t moment.
The simulation description will be divided into two scenarios in conjunction with equation (12) and the aforementioned simulation conditions. The carrier in the scene one is provided with two navigation sources of a navigation source 1 and a navigation source 2, the carrier in the scene two is provided with three navigation sources of the navigation source 1, the navigation source 2 and a navigation source 3, and position information measured by each navigation source, fusion information obtained by fusing the position information and a corresponding error curve are respectively simulated in the two scenes. Fig. 3 and 4 are a navigation track and an error curve in a scene one, respectively, and fig. 5 shows specific numerical values of an error in the scene one; fig. 6 and 7 are a navigation track and an error curve in a second scene, respectively, and fig. 8 shows specific values of the error in the second scene. Compared with the simulation graphs, the fusion positioning method based on the information probability provided by the invention has the advantages that after the position track information measured by each navigation source is fused, the overall positioning precision can be effectively improved; and as the number of the integrated navigation sources is increased, the integral integrated positioning precision is also improved even if the navigation sources with low positioning precision are added.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (4)

1. A fusion positioning method based on information probability is characterized in that: the method comprises the following steps:
step 1: for n navigation sources loaded on a carrier, establishing a probability statistical model of the positioning information of each navigation source, and determining a probability density function of the positioning information of each navigation source; the probability density function is based on a gaussian distribution;
step 2: the carrier runs for a period of time T-1, 2, …, T, and the motion trail sequence of the carrier measured by the ith navigation source is Xi＝{xi1,xi2,…,xiT}，i＝1,2,…,n；
And step 3: calculating a fusion product factor S between every two navigation sources by using the probability density function of the positioning information of each navigation source determined in the step 1 and the motion trail sequence of the carrier measured by each navigation source in the step 2 through the following formulaab
Figure FDA0002890486430000011
Wherein the content of the first and second substances,
Figure FDA0002890486430000012
and
Figure FDA0002890486430000013
for the variance, x, of the probability density function of the two navigation sources a and b to be calculatedaAnd xbPositioning the measured values for the navigations corresponding to the two navigation sources a and b;
if more than s fusion product factors in the fusion product factors between a certain navigation source and other navigation sources are lower than a set threshold value, the navigation source is considered to have larger deviation in the task, and the data corresponding to the navigation source is removed before the subsequent fusion calculation is carried out, so that the navigation source does not participate in the subsequent fusion calculation;
and 4, step 4: after all navigation sources are processed in step 3, the formula is utilized
Figure FDA0002890486430000014
Calculating to obtain a carrier position coordinate P obtained by fusion at the t-th momentt(ii) a Wherein m is the number of the navigation sources subjected to fusion after the processing of the step 3, and xitVehicle position information measured at time t for the ith navigation source.
2. The fusion positioning method based on information probability as claimed in claim 1, wherein: in step 3, s takes the value of 2.
3. The fusion positioning method based on information probability as claimed in claim 1, wherein: in step 1, when the navigation source is a navigation source with known positioning accuracy, the standard deviation RMS is calculated to be RMS of 1.2 × CEP according to the circular probability error CEP of the navigation source, and the corresponding variance σ is further obtained2＝1.44*CEP2。
4. The fusion positioning method based on information probability as claimed in claim 1, wherein: in step 1, when the navigation source is the navigation source with unknown positioning accuracy, a fixed-point repeated experiment method is adopted to obtain the positioned data distribution, the circular probability error CEP of the navigation source is determined, then the standard deviation RMS is calculated to be 1.2 CEP, and the corresponding variance sigma is further obtained2＝1.44*CEP2。
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